Re: mac mini or imac?
The advantage of the iMac is that the integrated screen and included components make the package cheaper overall than if you need to buy EVERYTHING with the Mac Mini. And, obviously, at the higher price points it simply has better specs overall. The Mac Mini is a fantastic (and affordable) machine if you already have all your components (keyboard, monitor, mouse, etc) and just want to swap it in. I'm personally reluctant to tie my computer up with my monitor so I prefer to stick with Mac Minis over the iMacs. I've probably spent more money overall on my Mini than I would have on an iMac but I can also swap out my monitor at my leisure so that is worth it to me.
If you are only planning to do basic video edits and film touchup (i.e. you don't need more powerful software than the two programs you mentioned) you will probably find the base model of the Mac Mini sufficiently powerful for your needs. However, I would recommend against purchasing the current Mac Mini as rumors are flying that we will soon get a refresh of the unit with the new Haswell CPUs. Among other things, the new CPU should provide a significantly better integrated graphics chip so it will be worth the wait.
You will want to save some money in your budget for an external disc drive. I use the Apple SuperDrive. It's a great device that looks good connected up to the Mini but if you are interested in saving money, Other World Computing has some great devices like this one that can do the same job. I do recommend that you invest in a better hard drive as the 5400 RPM HDD on the entry level Mac Mini is a noticeable bottleneck. If you are buying from Apple, this will require you to purchase the more expensive i7 model as they don't offer HDD configurations with the entry level unit. You can do an install on your own as well (it is cheaper) but that requires a moderately high level of expertise as it involves disassembling the entire computer.
You might also be pleased by the performance you'll get from a Macbook Air. You can easily dock the Air to a desktop setup and use it as a desktop PC. It has specs right around what would be good for you (newer Haswell CPUs + SSD memory) without being as expensive as the iMac. It is a good bridge between the basic features of the current Mac Mini and the more powerful features of the iMac.
I will say that I own the entry-level Mac Mini myself and I have not been unhappy with the performance I've gotten from it. I push it pretty hard playing 3D games at times and the only significant issue I experience is long load times from that dreadful stock HDD. If you don't mind waiting a few seconds for it to load things up, it's a non issue. (If you're coming from Windows it's faster than business as normal over there anyway LOL!)
I hope this helps